Activity Overview
This activity explores special cases of the product rule where the 'shortcut' works. Through a series of examples and non-examples, students identify a pattern and then search for other patterns.
Objectives
The aim of this activity is to highlight two things:
- When product rule short-cuts work (minority)
- When the product rule needs to be used in its entirity. (majority)
In so doing, students gain a better understanding of the product rule and are less likely to take eroneous short cuts!
Vocabulary
- Product Rule
- Function
- Derivative
- Parameter
About the Lesson
Sometimes the derivative of f(x)g(x) is as simple as f'(x)g'(x). What do these functions look like, how and why do they work in this way. What is the general pattern. This activity explores examples (and non-examples) and progresses towards a general formula via carefully selected examples.